$k$ -喷流场论中的超应力
Hyper-Stresses in $k$-Jet Field Theories
摘要：
对于高阶连续介质力学和经典场论的配置被建模为一般纤维束的部分和广义速度被建模为其变化。光滑应力场被认为是三个不同的数学应力对象发挥的作用，传统的应力张量连续介质力学在欧氏空间。这些物体被称为变分超应力，牵引超应力和非完整应力。研究了这三种受力对象的性质及其相互关系。
英文摘要：
For high-order continuum mechanics and classical field theories configurations are modeled as sections of general fiber bundles and generalized velocities are modeled as variations thereof. Smooth stress fields are considered and it is shown that three distinct mathematical stress objects play the roles of the traditional stress tensor of continuum mechanics in Euclidean spaces. These objects are referred to as the variational hyper-stress, the traction hyper-stress and the non-holonomic stress. The properties of these three stress objects and the relations between them are studied.
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